An Asymptotic-Preserving IMEX Method for Nonlinear Radiative Transfer Equation

We present an asymptotic preserving method for the radiative transfer equations in the framework of P-N method. An implicit and explicit numerical scheme is proposed to solve the P-N system based on the order analysis of the expansion coefficients of the specific intensity, where the order of each expansion coefficient is derived by the Chapman-Enskog method. The coefficients at higher-order are treated explicitly while those at lower-order are treated implicitly in each equation of the P-N system. Energy inequality is proved for this numerical scheme. Several numerical examples validate the efficiency of this scheme in both optically thick and thin regions.

Automated summary

In this paper, an asymptotic preserving method is presented for solving the radiative transfer equations using the P-N method. The order analysis of expansion coefficients is conducted to propose an implicit and explicit numerical scheme for the P-N system. The efficiency of this scheme is validated through numerical examples in both optically thick and thin regions.